Question

Taking A = 30°, verify that
cos* A - sin* A = cos 2A.
​

Answer 1

Hi if A=30° then

Cos2A =cos^2 A - sin^2 A=2cos^2 A -1

cos 60°=cos^2 30°- sin^2 30° =2cos^2 30° -1

1/2 =(√3/2)^2 - (1/2)^2= 2(√3/2)^2 -1

1/2=3/4-1/4=2(3/4)-1

1/2=2/4=3/2 -1

1/2=1/2=1/2

hence verified

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Answer 2

Answer:

cos30-sin30=\cos60

(√3/2)-(1/2)2=1/2

3/4-1/4=1/2

2/4=1/2

1/2=1/2

hence proved